1. Field of the Invention
The present invention relates to a pressure-type flow rate control apparatus for use mainly in semiconductor manufacturing facilities and chemical plants. More specifically, this invention concerns an improved pressure-type flow rate control apparatus in which the flow rate of a fluid which is supplied at sub-sonic speeds is determined accurately using a new empirical formula, and then the flow rate of the fluid to be supplied is controlled accurately on the basis of this empirical formula.
2. Description of the Prior Art
In semiconductor manufacturing facilities, chemical plants, etc., a plurality of gaseous reactants are supplied at respective specific rates and are normally reacted in a reactor to produce an object or target gas. In this process, if the reactant gases are not supplied at accurate flow rates, then the chemical reaction proceeds unevenly, and as a result, unreacted gases remain in the produced object gas.
Reactant gases remaining unreacted become impurity gases and lower the purity of the object gas. Where such an unreacted gas is explosive, there is a particular concern that explosions may occur in subsequent facilities, and accordingly special measures are adopted to remove the explosive unreacted gas.
It is therefore necessary to control accurately the flow rates of gases to be supplied, and a mass flow controller has been used as gas flow rate controller at many plants. However, a mass flow controller has many problems; for instance, 1) a relatively slow response time, 2) poor flow rate accuracy at low flow rates, 3) numerous operational difficulties, and 4) high costs.
For this reason, it has been previously observed that there is a need to improve the accuracy of gas flow rate control by means other than a mass flow controller. In response, the present inventors developed a pressure-type flow rate control apparatus and disclosed the same in unexamined Japanese patent application no. 10-55218. In this pressure-type flow rate control apparatus, fluid is forced through an orifice under critical conditions such that the flow velocity of the fluid is super-sonic.
FIG. 5 is an explanatory diagram of a theoretical formula that has been used hitherto for calculating the flow rate of fluid. Below is discussed a case where a fluid flowing into an orifice through a pipe has an upstream pressure upstream of the orifice which is set at P1, and is supplied to a downstream pipe at a downstream pressure of P2; here the upstream pressure P1 and the downstream pressure P2 are expressed in absolute pressure values.
It is known that the flow rate conditions of the fluid passing the orifice change greatly once the flow velocity of the fluid reaches the speed of sound. Under non-critical (sub-sonic) conditions, before sonic velocity is reached, the downstream flow rate Q is given by:Q=SC(P2(P1−P2))1/2/T1/2,                but under critical (sonic) conditions, once sonic velocity has been reached, it is found that the formula:Q=SCP1/T1/2        holds good and is applicable;        wherein T is the absolute temperature of the fluid at the time of passing the orifice;        S is the sectional area of the orifice hole;        and C is a proportional coefficient.        
It is known in hydrodynamics that the critical conditions at which the velocity of a fluid reaches sonic velocity are expressed by the critical value rc of pressure ratio P2/P1. The critical value rc is given by P2/P1=rc=(2/(n+1)n/(n−1), using the gas specific heat ratio n.
Said specific heat ratio n is given by:                n=Cp/Cv,        where Cp is the specific heat capacity of the fluid at constant pressure,        and Cv is the specific heat capacity of the fluid at constant volume.        
In the case of two-atom molecular gases (e.g. O2, H2), n=7/5=1.4, and rc=0.53. In the case of nonlinear, three-atom molecular gases, n=8/6=1.33 and rc=0.54. Thus these values may be expressed as rc=˜0.5.